2024 FMSS AMATH P1 PRELIM QP

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/01 Paper 1 Date: 21 August 2024 Duration: 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142. For Examiner’s Use Table of Penalties Question Number Presentation  1  2 Rounding off  1 Parent’s/Guardian’s Signature Setters: Mrs Lim CC and Ms Thio LH This question paper consists of 22 printed pages  90

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 2 Additional Mathematics Paper 1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21 221 , where n is a positive integer and ! )1)...(1( )!(! ! r rnnn rnr n r n +−−=−=      2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += cosec 2 A = 1 + cot 2 A BABABA sincoscossin)sin( = tan tantan( ) 1 tan tan ABAB AB += − sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − A AA 2tan1 tan22tan −= Formulae for ABC sin sin sin a b c A B C== Abccba cos2222 −+= cos( ) cos cos sin sinA B A B A B= 1 sin2 ab C=

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 3 Additional Mathematics Paper 1 Answer all the questions. 1 (i) Express 24 8 5xx+− in the form 2()p x q r++ , where p , q and r are constants to be found. [3] (ii) Hence, state the coordinates of the turning point of the curve 24 8 5y x x= + − . [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 4 Additional Mathematics Paper 1 2 Without using a calculator, find the values of a and b for which the solution of the equation 24 3 6xx =+ is 7 ab+ . [5]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 5 Additional Mathematics Paper 1 3 Points A, B, C and D lie on a circle. The tangent to the circle at A meets BD produced at E. AE is parallel to BC. Prove that (i) AB = AC, [3] (ii) = 2CDE ABC . [3]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 6 Additional Mathematics Paper 1 4 (a) The diagram shows part of the graph of tan .y a bx c=+ The graph has vertical asymptotes at 4x =− and 4x = and passes through the points P and Q. (i) Explain why 1 8b= . [2] (ii) Hence find the equation of the curve. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 7 Additional Mathematics Paper 1 (b) The function f ( )x is defined by f ( ) 4 3sin 2xx=+ for 0 360x   . Sketch the graph of f ( )yx= on the axes below. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 8 Additional Mathematics Paper 1 5 The diagram shows a shape made by cutting an equilateral triangle out of a rectangle of width x cm. The perimeter of the shape is 20 cm. (i) Show that the area, A cm2, of the shape is given by 26310 4A x x  +=−  . [3]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 9 Additional Mathematics Paper 1 (ii) Given that x can vary, find the value of x which produces the maximum area and calculate this maximum area. Give your answers to 2 significant figures. [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 10 Additional Mathematics Paper 1 6 (a) Express ( )( ) 2 8 13 1 2 2 x xx + ++ in partial fractions. [5]